Optimal signal processing for twisted pair transceivers

ABSTRACT

A receiver that easily receives signals from transmission channels having long cable lengths is presented. The receiver includes an analog pre-filter that removes distortions and intersymbol interference from a predetermined transmission channel. The analog pre-filter is coupled with a digital receiver that provides digital equalization. The combination of analog equalization with digital equalization allows for simplified digital equalization while retaining the versatility of digital signal processing.

BACKGROUND

1. Field of the Invention

This invention relates to digital communication systems and, more particularly, to an optimal architecture for receiver processing.

2. Background

The dramatic increase in desktop computing power driven by intranet-based operations and the increased demand for time-sensitive delivery between users has spurred development of high speed Ethernet local area networks (LANs). 100 BASE-TX Ethernet (see IEEE Std. 802.3u-1995 CSMA/CD Access Method, Type 100 Base-T) using existing category 5 (CAT-5) copper wire, and the newly developing 1000 BASE-T Ethernet (see IEEE Draft P802.3ab/D4.0 Physical Layer Specification for 1000 Mb/s Operation on Four Pairs of Category 5 or Better Twisted Pair Cable (1000 Base-T)) for Gigabit/s transfer of data over category 5 data grade copper wiring, require new techniques in high speed symbol processing. On category 5 cabling, gigabit per second transfer can be accomplished utilizing four twisted pairs and a 125 megasymbol/s transfer rate on each pair where each symbol represents two bits.

Physically, data is transferred using a set of voltage pulses where each voltage represents one or more bits of data. Each voltage in the set is referred to as a symbol and the whole set of voltages is referred to as a symbol alphabet.

One system of transferring data at high rates is Non Return to Zero (NRZ) signaling. In NRZ, the symbol alphabet {A} is {−1, +1}. A logical “1” is transmitted as a positive voltage while a logical “0” is transmitted as a negative voltage. At 125 M symbols/s, the pulse width of each symbol (the positive or negative voltage) is 8 ns.

An alternative modulation method for high speed symbol transfer is MLT3 and involves a three level system. (See American National Standard Information system, Fibre Distributed Data Interface (FDDI)—Part: Token Ring Twisted Pair Physical Layer Medium Dependent (TP-PMD), ANSI X3.263:199X). The symbol alphabet for MLT3 is {A}={−1, 0, +1}. In MLT3 transmission, a logical 1 is transmitted by either a −1 or a +1 while a logic 0 is transmitted as a 0. A transmission of two consecutive logic “1”s does not require the system to pass through zero in the transition. A transmission of the logical sequence (“1”, “0”, “1”) would result in transmission of the symbols (+1, 0, −1) or (−1, 0, +1), depending on the symbols transmitted prior to this sequence. If the symbol transmitted immediately prior to the sequence was a +1, then the symbols (+1, 0, −1) are transmitted. If the symbol transmitted before this sequence was a −1, then the symbols (−1, 0, +1) are transmitted. If the symbol transmitted immediately before this sequence was a 0, then the first symbol of the sequence transmitted will be a +1 if the previous logical “1” was transmitted as a −1 and will be a −1 if the previous logical “1” was transmitted as a +1.

The detection system in the MLT3 standard, however, needs to distinguish between 3 levels, instead of two levels as in a more typical two level system. The signal to noise ratio required to achieve a particular bit error rate is higher for MLT3 signaling than for two level systems. The advantage of the MLT3 system, however, is that the energy spectrum of the emitted radiation from the MLT3 system is concentrated at lower frequencies and therefore more easily meets FCC radiation emission standards for transmission over twisted pair cables. Other communication systems may use a symbol alphabet having more than two voltage levels in the physical layer in order to transmit multiple bits of data using each individual symbol. In Gigabit Ethernet over twisted pair CAT-5 cabling, for example, 5-level pulse amplitude modulated (PAM) data can be transmitted at a baud rate of 125 Mbaud. (See IEEE Draft P802.3ab/D4.0 Physical Layer Specification for 1000 Mb/s Operation on Four Pairs of Category 5 or Better Twisted Pair Cable (1000 Base-T)).

Therefore, there is a necessity for a receiver capable of receiving signals having large intersymbol interference from long transmission cables. There is also a necessity for reducing the difficulties associated with digital equalization of signals with large intersymbol interference without losing the versatility in the equalizer that is required to optimize the receiver.

SUMMARY OF THE INVENTION

In accordance with the invention, a receiver where signal equalization is partitioned into an analog pre-filter coupled to a digital receiver is presented. At least some of the intersymbol interference is removed from the signal by an analog pre-filter before the signal is received and processed through a digital equalizer. Signals having a large amount of intersymbol interference, such as those transmitted through long cables, are preprocessed through the pre-filter, reducing the difficulties of digital equalization without losing the versatility of the digital equalizer.

Embodiments of the invention can include any equalization scheme, including linear equalization, decision feed-back equalization, trellis decoding and sequence decoding, separately or in combination. Embodiments of the invention may also include cable quality and cable length indication and baseline wander corrections. Further, embodiments of receivers according to the present invention can also include echo cancellation and NEXT cancellation.

These and other embodiments of the invention are further explained below along with the following figures.

DESCRIPTION OF THE FIGURES

FIG. 1A shows a receiver system with an entirely digital equalizer.

FIG. 1B shows a receiver system with an entirely analog equalizer.

FIG. 2A shows a receiver system according to the present invention.

FIG. 2B shows an analog model of a transmission channel.

FIG. 3A shows an example transfer function representing a transmission channel.

FIG. 3B shows the exponential component of the signal distortion.

FIG. 3C shows an example transfer function of a pre-filter according to the present invention.

FIG. 3D shows the combined influence of the functions shown in FIGS. 3A, 3B and 3C on an input signal.

FIG. 4 shows a discrete time model of signal transmission through a transmission channel in combination with a pre-filter according to the present invention.

FIG. 5A shows another embodiment of a receiver according to the present invention.

FIG. 5B and 5C show embodiments of pre-filters for a receiver according to the present invention.

FIGS. 6A, 6B, 6C, 6D and 6E show embodiments of a multi-wire receiver system according to the present invention.

In the Figures, elements having similar or identical functions may have identical identifiers.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1A shows a block diagram of a typical transmission system 100 for a single-wire transmission channel. Transmission system 100 includes transmitter 107, transmission channel 102 and receiver 103. Transmitter 107 transmits a symbol stream {a_(k)} and can perform some signal shaping on the waveform formed by symbol stream {a_(k)}. Transmission channel 102 can be any transmission medium and distorts the transmitted waveform, creates intersymbol interference, and adds noise to the transmitted signal. Receiver 103 receives the transmitted signals from transmission channel 102. Receiver 103 includes an analog-to-digital converter (ADC) 104 and equalizer 106 connected in series. In receiver 103 of FIG. 1A, the equalization of an input signal to receiver 103 is accomplished digitally. Digital equalization becomes problematic as the cable length increases due to the large intersymbol interference associated with longer cables.

In general, a signal received by receiver 103 will include contributions from several transmitted symbols as well as noise and channel distortions. Each symbol transmitted is diffused in the transmission process so that it is commingled with symbols being transmitted at later transmission times. This effect is known as “intersymbol interference” (ISI). (See E. A. LEE AND D. G. MESSERCHMITT, DIGITAL COMMUNICATIONS (1988)).

Intersymbol interference is a result of the dispersive nature of the communication channel. The IEEE LAN standards require that systems be capable of transmitting and receiving data through at least a 100 meter cable. In a 100 meter cable, the signal strength at the Nyquist frequency of 62.5 Mhz is reduced nearly 20 db at the receiving end of the cable. Given this dispersion, a single symbol may affect symbols throughout the transmission cable of transmission channel 102.

A digital representation of an input signal to receiver 103 at sample time k, neglecting channel distortion and noise, can be represented as

x _(k) =C ₀ a _(k) +C ₁ a _(k−1) + . . . +C _(j) a _(k−j) . . . ,   (1)

where a_(k−j) represents the (k−j)th symbol in the symbol sequence and C_(j) represents the contribution of the (k−j)th symbol to signal x_(k). Equalizer 106 receives digitized sample x_(k) and deduces currently received symbol â_(k) by, usually adaptively, removing the contribution of previous symbols a_(k−j) from detected sample x_(k) (i.e., removing the intersymbol interference). The deduced symbol â_(k) represents the best estimation by receiver 103 as to what the transmitted symbol a_(k) was.

However, with long cable lengths, the contribution of earlier received symbols becomes significant. For example, with cable lengths above about 100 meters, C₁ can be as high as 0.95 (i.e., 95% of symbol a_(k−1) may be represented in the input signal). Contributions from other previous symbols can also be high. Given that equalizer 106 can not adjust for the contribution of symbols not yet received (i.e., the kth detected sample can not include contributions from the (k+1)th transmitted symbol), equalizer 106 would have a difficult time distinguishing the kth and the (k−1)th symbol under these circumstances. An adaptive receiver can have particular difficulty upon startup distinguishing contribution from the kth symbol from the contribution of the (k−1)th symbol and determining the equalizer parameters corresponding to the mixing parameters {C_(j)}.

Therefore, for large cable lengths a digital equalizer will be faced with deducing the current symbol from a sample containing significant contributions from numerous previously received symbols. The difficulty is not only deducing the symbols but in adaptively choosing the operating parameters of the equalizer in order to optimize the performance of receiver 103.

An alternative approach to digital equalization is analog equalization. FIG. 1B shows a block diagram of a transmission system 110 having an analog receiver 111 coupled to transmission channel 102. Receiver 111 includes an analog equalizer 112 having an analog filter tailored to remove intersymbol interference from the received signal. Although having the advantage of processing loop speed, equalizer 112 can not be adaptively optimized for the performance of receiver 111.

FIG. 2A shows a receiver system 200 according to the present invention. Receiver 200 includes a transmitter 221, a transmission channel 201 and a receiver 206. Transmitter 221 outputs a symbol stream {a_(k)} to transmission channel 201. Transmitter 221 can output symbol stream {a_(k)} directly or, in some embodiments of the invention, transmitter 201 can perform some pre-processing of the waveform formed by the sequential transmission of the symbol stream {a_(k)}.

Transmission channel 201 represents the transmission of a signal between transmitter 221 and receiver 206 and can include any transmission medium, including twisted copper, coaxial cable or optical fiber. The symbol stream {a_(k)} can be composed of any symbol alphabet, including NRZ, MLT3, PAM-5 (where the symbol alphabet is given by {−2,−1,0,1,2}) or any other symbol alphabet and modulation that are used in transceivers such as transmission system 200.

Transmission system 200 may be a portion of a larger transceiver system. In general, transceivers of this type may have any number of transmission channels similar to transmission channel 201. For example, gigabit per second transfer of data can be accomplished using four transmission channels, each with one twisted pair cable. Further, transmission channels such as transmission channel 201 can be bi-directional, i.e. transmitting data in both directions. For example, receiver 206 may be associated with a transmitter that transmits symbol streams to other receivers coupled to the same cable as is included in transmission channel 201. Any number of transmitters and receivers may be coupled to the cable associated with transmission channel 201. Each coupling may affect the response of transmission channel 201.

The transmitted symbols in the sequence {a_(k)} are members of the symbol alphabet {A}. In the case of PAM-5 signaling, for example, the symbol alphabet {A} is given by {−2, −1, 0, +1, +2}. The index k represents the time index for that symbol, i.e. at sample time k, the symbol being transmitted to transmission channel 201 is given by a_(k). Notationally, a particular symbol in clock cycle k is denoted without brackets as a_(k) whereas the symbol sequence is denoted with brackets as {a_(k)}.

The real-time output of transmitter 221 can be represented as A_(s)(ω), where A_(s)(ω) is the Fourier transform of the analog signal a_(s)(t) that represents the symbol stream {a_(k)}. Therefore,

$\begin{matrix} {{A_{s}(\omega)} = {\int_{- \infty}^{\infty}{{a_{s}(t)}^{{- }\; \omega \; t}\ {{t}.}}}} & (2) \end{matrix}$

Signal a_(s)(t) also represents the effects of any pre-shaping that may be performed by transmitter 221.

The output signal from transmission channel 201, now treated as an analog signal, suffers from channel distortion, the addition of random noise, and a flat signal loss. The output signal from transmission channel 201 is input to receiver 206. As shown in FIG. 2B, transmission channel 201 can be modeled as having a linear, time invariant portion 202 with transfer function H_(s)(ω) and a noise portion represented as noise adder 203. The transfer function H_(s)(ω) includes the effects of transmit and receive transformers and the transmission medium (e.g., cable) on the transmitted signal. The input signal, A_(s)(ω), is related to the output signal of portion 202, X_(s)(ω) by the relationship

X _(s)(ω)=H _(s)(ω)A _(s)(ω).   (3)

The total output signal from transfer channel 201, then, is

Y _(s)(ω)=H _(s)(ω)A _(s)(ω)+n _(s)(ω),   (4)

where n_(s)(ω) is a random noise component. Equations (3) and (4) assume a linear, time invariant transmission system.

The output symbol from transfer channel 201, then, is Y_(s)(ω). For long cable lengths, the intersymbol interference contained in signal Y_(s)(ω) can be severe, including significant portions of previously transferred symbols in Y_(s)(ω). For example, for a cable length of above about 100 meters the contribution of the last sent symbol to the currently received signal may be as high as 95%. Pre-filter 207 can remove a significant portion of the intersymbol interference created by transmission channel 201.

Pre-filter 207 receives signals from transmission channel 201 and pre-shapes them for input to digital filter 208. The pre-shaping performed by pre-filter 207 can include partial removal of intersymbol interference so that less intersymbol interference remains to be removed by digital equalizer 212.

Pre-filter 207 can be designed based on frequency-sampling methods in which a desired frequency response is uniformly sampled and filter coefficients are then determined from these samples using an inverse discrete Fourier transform. For example, one embodiment of pre-filter 207 includes a 1-zero, 2-pole filter having a frequency response of approximately the inverse of, for example, the transfer function H_(s)(ω) associated with a 50 meter cable (CAT-5) in combination with any pre-shaping that may have been performed by transmitter 221. Pre-filter 207, therefore, can be fixed to remove the influence of intersymbol interference from a given cable configuration, e.g. a twisted-copper pair having a particular length. Variations in the intersymbol interference inherent in variations of the cable or length from that expected can be accommodated by adaptive functions in digital equalizer 212.

Although pre-filter 207 can be any number of filters coupled in series, pre-filter 207 can be represented with a transfer function H_(PF)(ω) that represents the effects on an input signal of all of the filters in pre-filter 207. Therefore, assuming that pre-filter 207 is linear and time-invariant, the output signal Z_(s)(ω) from pre-filter 207 is given by

Z _(s)(ω)=GH _(PF)(ω)Y _(s)(ω),   (5)

where G is the analog gain of analog amplifier 222. The transfer function that represents the combination of transmission channel 201 and pre-filter 207 is given by

H _(T)(ω)=GH _(s)(ω)H _(PF)(ω).   (6)

Ideally, if pre-filter 207 completely compensates for transmission channel 201, the total transfer function, H_(T)(ω)=G_(HS)(ω)H_(PF)(ω), is unity. In a practical transmission system, the transfer function H_(PF)(ω) of pre-filter 207 is determined by inverting the predicted or measured transfer function H_(s)(ω) of transmission channel 201.

The frequency response(FR) of a complete channel, i.e. transmission system 200 including transmission channel 201, and digital filter 208, neglecting random noise n_(s)(ω) and not including the frequency response of prefilter 207, can be modeled as

H _(c)(f,l)=H _(PR)(z)H _(s)(f,l)H _(EQ)(z)gG H _(co)(f)   (7)

where H_(PR)(Z) is the partial-response shaping accomplished by transmitter 221 before transmission, z=e^(jπT), ω=2πf, and T is the symbol (and sampling) interval. H_(s)(f,l) is the frequency response of transmission channel 201, e.g. of the CAT-5 cable, of length l and the transmit and receive transformers. In one embodiment, the partial response shaping H_(PR)(Z)=0.75+0.25Z⁻¹. H_(EQ)(z) is the transfer function of digital equalizer 212. In one embodiment, H_(EQ)(Z) is chosen to be c⁻¹Z+c_(o)+c₁Z⁻¹, although in general H_(EQ)(Z) is given by

${\sum\limits_{k = {- N}}^{M}\; {c_{k}Z^{- k}}},$

where N and M are positive integers. The parameter g is the gain output from automatic gain control (AGC) 215. H_(co)(f) represents the frequency response of the remaining elements of a complete channel, e.g. the digital-to-analog pulse (which can be a rectangular pulse of length T or a trapezoidal pulse with rising and falling edges of length T/2 and flat portion of length T/2) and other elements of transmission channel 201.

The frequency response of transmission channel 201, H_(s)(ω,l), is a function of cable length l. Both gain g and H_(EQ)(Z) will depend on cable length l. The gain g is increased for increased cable length due to increased signal loss. The parameters c⁻¹, c₀, and c₁ of H_(EQ)(Z) also depend on cable length l. H_(co)(f) is not a function of cable length l.

Examples of the frequency response for system 200 are shown in FIGS. 3A through 3D. FIG. 3A shows the transfer function of transmission channel 201 which approaches zero asymptotically. FIG. 3B shows signal e^(−ωτ). FIG. 3C represents the transfer function of pre-filter 207. FIG. 3D represents the total frequency response or the product of the signals represented in FIGS. 3A, 3B and 3C.

The frequency response of the complete channel, H_(c)(f), does not include the effects of prefilter 207. The analog prefilter 207 can be represented by H_(PF)(s)=(b₁s+1)/(a₂s²+a₁s+1), where s=jw. H_(PF)(s), therefore, is characterized by the filter parameters b₁, a₁, and a₂. H_(PF)(S) can be determined by minimizing a cost function that is related to the total intersymbol interference found in transmission system 200.

A measure of the intersymbol interference due to the comparison of the folded spectrum with a flat spectrum can be expressed as

E(l)=∫_(1/2T) ^(1/2T) |[H _(c)(f,l)H _(PF)(s)e ^(jωτ)]_(fold)−1|² df.   (8)

The parameter τ is the timing phase difference between the transmitter digital to analog converter and the receiver analog-to-digital converter (ADC 210), as calculated by clock recovery 216. The integral in Equation (8) represents the inverse discrete Fourier transform of all signals received in one period, e.g. −0.5/T to 0.5/T. The folded spectrum in the integral can be described by spectrum folding, which can be defined as

$\begin{matrix} {{\left\lbrack {X(f)} \right\rbrack_{fold} = {\frac{1}{T}{\sum\limits_{k}\; {{X\left( {f - \frac{k}{T}} \right)}.}}}},} & (9) \end{matrix}$

where X(f) is any general function of frequency.

In one embodiment, the transfer function of analog pre-filter 207, H_(PF)(s), is obtained by minimizing the cost function

$\begin{matrix} {C = {{\sum\limits_{k = 1}^{K}\; {w_{k}{E\left( l_{k} \right)}}} + {w_{K + 1}P}}} & (10) \end{matrix}$

with respect to the filter parameters b₁, a₁, and a₂. The first K terms are a measure of Intersymbol Interference at cable lengths l₁, l₂, . . . l_(K). In one embodiment, K=3. Although in general, any number of cable lengths K can be used, if K is 1 minimizing the cost function will result in a filter that is optimized for only one cable length. Alternatively, using too many cable lengths complicates the optimization. The last term in Equation (10),

P=∫ _(1/2T) ^(∞) |H _(PF)(s)‥² df   (11)

imposes an additional penalty on the high frequency components of H_(PF)(S). The high frequency penalty P operates to attenuate high frequency echos. Other factors can be included in a cost function, for example a term to reduce quantization noise can be added. This quantization term would be proportional to

g√{square root over (c₁ ²+c₂ ²+ . . . +c_(K) ²)}.

Each term in the cost shown in Equation (10) is weighted by a weight factor w_(i). These weights specify the importance of each term. The weights are chosen such that the peak magnitude of H_(PF)(s) is not too large and so that H_(PF)(s) is small at high frequencies. The analog prefilter 207 determined by H_(PF)(s) found by optimizing the cost function (10) minimizes the intersymbol interference for cable lengths l₁ through l_(K) and attenuates high frequency echo signals.

As previously described, H_(s)(ω,l), gain g, and H_(EQ)(Z) all depend on cable length l. Additionally, the output from clock recovery 216, τ, also depends on cable length l. Therefore, E(l₁) through E(l_(K)) are all different. The parameters G, g, τ, and equalizer parameters in H_(EQ)(Z) (e.g., c⁻¹, c₀, and c₁) in E(l₁) through E(l_(K)) are those parameters that the adaptive loops in analog gain control 220, gain control 215, clock recover 216, and coefficient update 214, respectively, would converge for cable lengths l₁ through l_(K), respectively.

Minimizing E(l) with respect to b₁, a₁, and a₂ would yield an H_(PF)(s) for prefilter 207 which can produce a flat folded spectrum if the cable length is l. However this is based on the assumption that the actual equalizer parameters for H_(EQ)(Z), analog gain G, digital gain g, and timing phase τ are the same as those used in the equation for E(l). If they are different, the results are less useful.

The better determination of equalizer parameters for H_(EQ)(Z), gain g, and timing phase τ can be found by an iterative procedure as described below, resulting in determination of prefilter function H_(PF)(s). With an initial choice of equalizer parameters for H_(EQ)(Z), gain g, and timing phase τ, the cost function C is minimized to determine an H_(PF)(s). Using this H_(PF)(s) the equalizer parameters for H_(EQ)(Z), gain g, and timing phase τ can be determined for each cable length l₁ through l_(K). Using these new sets of equalizer parameters for H_(EQ)(Z), gain g, and timing phase τ (one set of parameters for each cable length l₁ through l_(K)) in the cost function C, H_(PF)(s) is recomputed. This process is repeated until there are no significant changes between successive iterations. In other words, the above procedure will converge to a particular set of filter parameters for H_(PF)(s) that determines prefilter 207.

In one case H_(s)(ω) includes the frequency response of the transmit and receive transformers, each of which is modeled as a first order transfer function with −3 dB cutoff at 100 MHz. Additionally, transmission channel 201 is category-5 twisted copper pair cable, H_(EQ)(Z)=c⁻¹Z+c₀+c₁Z⁻¹, H_(PR)(Z)=0.75+0.25Z⁻¹, and T=8 ns. The optimization of the cost function C in Equation 10 with K=3 and cable lengths l₁=0 m, l₂=50 m, l₃=120 m leads to a filter function for prefilter 207 described by

$\begin{matrix} {{{H_{PF}(s)} = {\frac{{0.8077\hat{s}} + 1}{{0.1174{\hat{s}}^{2}} + {0.1255\hat{s}} + 1}.}},} & (12) \end{matrix}$

where ŝ=sT.

Alternatively, pre-filter 207 can be an adaptive analog filter. An adaptive analog filter can be a filter function of the form

H _(PF)(s)=(1−V _(c))+V _(c) PF(s)   (13)

and is controlled by the single parameter V_(c). The paramter V_(c) is varied in the range 0<V_(c)<1 to achieve partial equalization for various cable lengths. If V_(c)=0, H_(PF)(s)=1 (unity), i.e. no equalization performed by prefilter 207. If V_(c)=1 then H_(PF)(s)=PF(s), i.e. maximum equalization attainable by the filter structure defined by PF(s) for prefilter 207. As V_(c) is varied linearly from 0 to 1, H_(PF)(S) varies from unity to PF(s).

PF(s) can be a band-pass or a high-pass filter. Therefore, the peak magnitude of the frequency response of H_(PF)(s) increases with increasing V_(c). If PF(s) performs suitable equalization for a particular cable length l_(o), the filter with V_(c)<1 would perform suitably for cable lengths l<l_(o). Hence V_(c) is monotonic with cable length.

For example, PF(s) can have one zero and 2 poles (complex-conjugate pair) in the form

$\begin{matrix} {{{{PF}(s)} = {\frac{\omega_{n}^{2}}{\omega_{z}} \cdot \frac{s + \omega_{z}}{s^{2} + {2{\delta\omega}_{n}s} + \omega_{n}^{2}}}},} & (14) \end{matrix}$

where ω_(z) is the zero frequency, ω_(n) is the pole frequency, and δ is the damping factor.

At low frequency, the filter described by Equation 14 starts from unity and rolls off as 1/s at high frequencies. Hence the filter passes less noise and high frequency echo. Moreover, a small order PF(s) would require less number of resistors, capacitors, and operational amplifiers to realize the circuit, which implies less sources of circuit noise and also easier and cheaper implementation for prefilter 207. In another embodiment, PF(s) is the optimized analog filter function that optimizes the cost C described in Equation 10 for one length where the length is the maximum targeted cable length. V_(c) can be adapted, then, to shorter cable lengths.

To minimize the peak magnitude of the filter structure H_(PF)(s), two stages of filter structures namely, H_(PF)(s)=H₁(s)H₂(s) where H₁(s) and H₂(s) are cascaded can be utilized. In this case,

H ₁(s)=(1−V _(c1))+V _(c1) PF(s),   (15)

and

H ₂(s)=(1−V _(c2))+V _(c2) PF(s).   (16)

For example, PF(s) could be a one-zero two-poles filter with the zero at 30 MHz and complex-conjugate pair poles at 70 MHz with damping factor of 0.4. That is, ω_(z)=2π×30×10⁶, ω_(n)=2π×70×10⁶, δ=0.4 in equation (14) above. A cascade of H₁(s) and H₂(s) each with the above PF(s) can provide good partial equalization for a wide range of cable lengths.

In one embodiment, the digital equalizer transfer function executed by equalizer 212 can be expressed in the form

H _(EQ)(z)=c ⁻¹ z+c ₀ +c ₁ z ⁻¹ +c ₂ z ⁻² + . . . +c _(K) z ^(−K)   (17)

The first two coefficients can be fixed (i.e., coefficient update 214 does not alter c⁻¹ or c₀). For example, the first two equalizer coefficients can be set to c⁻¹=−⅛, c_(o)=1. The remaining equalizer coefficients, c₁ through c_(K) are adaptively chosen by coefficient update 214. The parameter K can be any positive integer. For a fixed(non-adaptive) analog filter, equalizer coefficient cl decreases monotonically with cable length. Therefore, equalizer coefficient c₁ is a good indicator of cable length. Additionally, AGC gain g is also a good indicator of cable length. Equalizer coefficient c₁ or gain g can be compared to a threshold Th_(AEQ) and the result of that comparison used to adapt analog prefilter 207.

In FIG. 2A, a Phase Detector 217 executes an updating algorithm with equalizer coefficient c₁ in order to choose adaptive parameters for analog prefilter 207. In phase detector 217, a phase detection parameter can be calculated by

PD _(AEQ)=−(c ₁ −Th _(AEQ))   (18)

The amount of threshold determines how much equalization is performed in analog prefilter 207 and how much is performed in digital equalizer 212. In one example, c₁ varies between about −0.35 to about −1.0 and TH_(AEQ) is chosen to be about −0.4.

Phase detector 217 operates to control V_(c). In a cascading prefilter, phase detector 217 controls any number of adaptive parameters for analog filters, V_(c1) through V_(cN) where N is the total number of cascaded analog prefilters included in analog prefilter 207. One method of adaptively choosing a value for V_(c) (or each of V_(c1) through V_(cN)) is to increment or decrement the value of V_(c) based on whether the calculated parameter PD_(AEQ) is positive or negative. Alternatively, the parameter phase detector 217 may include an accumulator that inputs the calculated parameter PD and outputs a signal that controls V_(c).

Additionally, in receiver 208 of FIG. 2A, an analog AGC 220 is included that scales the input signal to digital filter 208 so that the entire dynamic range of ADC 210 is utilized while keeping the probability of saturation very low. Analog AGC 220 inputs the signal output of ADC 210 and outputs a signal to amplifier 222.

Analog AGC 220 outputs a signal to amplifier 222 which adjusts the output levels of prefilter 207 to optimize the functionality of ADC 210. In one embodiment, AGC 220 calculates a phase detector parameter for the loop, accumulates the results of the phase detect parameter calculation, and converts the accumulated phase detector parameter to an analog signal which is input by prefilter 207. The Phase Detector parameter for this loop can be defined as

PD _(AGC) [k]=α _(k,1)+α_(k,2),   (19)

where

$\begin{matrix} {\alpha_{k,1} = \left\{ \begin{matrix} {- 1} & {{{if}\mspace{14mu} {\alpha_{k}}} > {Th}_{AGC}} \\ 0 & {{otherwise},} \end{matrix} \right.} & (20) \\ {\alpha_{k,2} = \left\{ \begin{matrix} 1 & {{{if}\mspace{14mu} k\mspace{14mu} {mod}\mspace{14mu} N} = 0} \\ 0 & {{otherwise},} \end{matrix} \right.} & (21) \end{matrix}$

α_(k) is the output signal from ADC 210 during time period k, i.e. at time instant t=kT, and N is chosen to make use of the range of ADC 210.

At the convergence of the phase loop in AGC 220, i.e. the steady-state condition, the expected value of PD_(AGC) is 0. This ensures that the probability of |α_(k)|>Th is 1/N for any k. The threshold value Th_(AGC) and N are suitably chosen to make good use of the A/D range. For the application of Gigabit Ethernet, Th_(AGC) and N are chosen such that the probability of saturation of ADC 210 is lesser than about 10⁻⁶. In one example, Th_(AGC) is about 0.8 of the range of ADC 210, for example 50 in a 7 bit ADC, and N is about 1024.

In general, pre-filter 207 can be arranged to reduce or eliminate the intersymbol interference inherent in any length cable. Once a transfer function, such as that given in Equations 12 or 14, is determined for a particular configuration of transmission channel 201, one skilled in the art of filter design can construct the appropriate filter. Therefore, a transfer function such as that shown in Equations 12 and 14 completely describes an analog filter which can be utilized for equalization in pre-filter 207.

As shown in FIG. 2A, the analog signal output Z_(s)(ω) from pre-filter 207, which is the input symbol sequence {a_(k)} distorted by the transmission channel and filtered by pre-filter 207 in the above described fashion, is input to digital receiver 208. Receiver 208 can include an anti-aliasing filter 209, an analog to digital converter 210, a digital amplifier 211, an equalizer 212, and a slicer 213.

Anti-aliasing filter 209 receives analog signals from analog pre-filter 207. In most embodiments, anti-aliasing filter 209 is an analog low pass filter.

Analog to digital converter 210 is coupled to receive an output signal from anti-aliasing filter 209. Analog to digital converter 210 can have any accuracy, but in most embodiments a six to eight bit converter is utilized. By adding pre-filter 207, the linearity, i.e. the number of bits, requirements of ADC 210 is reduced. For example, by using a 50-meter cable (CAT-5) plus transmit shaping, as described above, the ADC requirements can be significantly reduced if receiver 206 includes a pre-filter implementing the transfer function described by Equation 8. The requirements of ADC 210 may be reduced from an 8-bit ADC to a 6-bit ADC at 125 Mega-samples/second, for example.

By reducing the linearity of the ADC requirements, in one embodiment a linear equalizer is used rather than a decision feedback equalizer or a more complicated trellis decoder. In addition, by using a pre-filter, critical timing loops normally associated with Gigabit receiver designs is eliminated. Experiment has shown that the time complexity of the critical path required to implement a 4D, 8-state trellis decoder in a Gigabit receiver is reduced. The reduction in complexity inherent in reducing the distortion in the signal input to digital receiver 208 can result in receivers having fewer components and simpler implementations.

A discreet-time model of the response of transmission channel 201 in combination with pre-filter 201 is shown in FIG. 4 and includes a channel response 204, represented by the channel function f(z). Noise adder 205 represents addition of a random noise factor n_(k) to the transmitted signal. The discreet-time model is particularly applicable for digital receiver 208. In which case, transfer function f(Z) is a folded spectrum of the combined frequency response of H_(PR)(Z)H_(s)(ω)H_(PF)(ω)H_(CO)(ω).

It is assumed that the channel model includes the effect of transmit and receive filtering. In addition, the transmission channel is assumed to be linear in that two overlapping signals simply add as a linear superposition. Therefore, the channel function polynomial of channel response 204 can be defined as

f(Z)=f ₀ +f ₁ z ⁻¹ +f ₂ z ⁻²+ . . . +f_(N) z ^(−N),   (22)

where f₀, . . . , f_(j), . . . , f_(N) are the polynomial coefficients representing the dispersed component of the (k−j)th symbol present in the a_(k)th symbol and N is a cut-off integer such that f_(j) for j>N is negligible. The polynomial f(Z) represents the frequency response of transmission channel 201 in combination with pre-filter 207. (Z⁻¹ represents a one symbol period delay) See A. V. OPPENHEIM & R. W. SCHAFER, DISCRETE-TIME SIGNAL PROCESSING 1989.

The noiseless output signal of transmission channel 201 at sample time k, i.e. the output signal from channel response 207, is then given by

x _(k) =f ₀ *a _(k) +f ₁ *a _(k−1) + . . . f _(N) *a _(k−N).   (23)

Thus, the channel output signal at time k depends, not only on transmitted data at time k, but past values of the transmitted data, i.e. there remains some intersymbol interference.

The noise element of the input signal, represented by noise adder 205, is represented by the sequence {n_(k)}. Therefore, the noisy output of the channel, i.e. the output signal from ADC 210, is given by

α_(k) =x _(k) +n _(k),   (24)

where the noise samples {n_(k)} are assumed to be independent and identically distributed Gaussian random variables (See E. A. LEE AND D. G. MESSERCHMITT, DIGITAL COMMUNICATIONS (1988)) with variance equal to σ².

Digital amplifier 211 amplifies the output signal from analog to digital converter 210, α_(k), to adjust for the loss of signal resulting from the transmission through transmission channel 201 and pre-filter 207.

Equalizer 212 can be any type of equalizer including a linear equalizer, a decision feedback equalizer, or a sequence detector, alone or in combination. Examples of equalizers applicable to 100 or 1000 BASE-T Ethernet over category-5 wiring, 24 gauge twisted copper pair, are discussed in “Improved Detection for Digital Communication Receivers,” U.S. application Ser. No. 08/974,450, filed Nov. 20, 1997, of Sreen Raghavan, assigned to the same assignee as the present application, herein incorporated by reference in its entirety; and “Simplified Equalizer for Twisted Pair Channel,” U.S. application Ser. No. 09/020,628, filed Feb. 9, 1998, by Sreen Raghavan, assigned to the same assignee as the present disclosure, herein incorporated by reference in its entirety.

Further examples of equalization systems are described in “Look-Ahead Maximum Likelihood Sequence Estimation,” U.S. application Ser. No. 09/296,086, filed Apr. 21, 1999, by Sreen Raghavan and Hari Thirumoorthy, assigned to the same assignee as the present application, herein incorporated by reference in its entirety; “Digital Baseline Wander Correction Circuit,” U.S. application Ser. No. 09/151,525, filed Sep. 11, 1998, by Sreen Raghavan, assigned to the same assignee as the present disclosure, herein incorporated by reference in its entirety; “Cable Length and Quality Indicator,” U.S. application Ser. No. 09/161,346, filed Sep. 25, 1998, by Sreen Raghavan and Doug Easton, assigned to the same assignee as the present disclosure, herein incorporated by reference in its entirety; and “Detector for an Ethernet Receiver,” by Peter J. Sallaway and Sreen Raghavan, Attorney Docket No. M-5628 US, filed on Apr. 28, 2000, herein incorporated by reference in its entirety.

Slicer 213 receives an input signal from equalizer 212 and, based on the input signal, decides on an output signal stream. The output signal stream {â_(k)} represents the best estimate of receiver 208 of the symbol stream {a_(k)} that was originally transmitted by transmitter 221.

Receiver 208 may be an adaptive receiver, further including a coefficient update 214 that adjusts the parameters to equalizer 212 in order to optimize the performance of receiver 208. Receiver 208 may also include an automatic gain control (AGC) 215 that dynamically adjusts the gain of amplifier 211 in order to maximize the efficiency of receiver 208. Furthermore, clock recovery 216 can provide timing and framing for analog to digital converter 210, representing an element of a phase-locked loop.

FIG. 5A shows another embodiment of a receiver 506 according to the present invention. Receiver 506 includes pre-filter 207, anti-aliasing filter 209, analog-to-digital converter 210, amplifier 211, and digital equalizer 212. Although digital equalizer 212 can be any equalizer system, as has been previously described, in FIG. 5A digital equalizer 212 is shown as having equalizer 511 coupled in series with trellis decoder 512. Equalizer systems are described in previously incorporated U.S. application Ser. Nos. 08/974,450, 09/020,628, 09/161,346, 09/296,086, 09/151,525, and [Attorney Docket No. M-5628 US] and will not be further discussed here.

Receiver 506 also includes adaptive coefficient update 214 which adaptively chooses the operating parameters of equalizer 511, gain control 215 which adaptively chooses the gain setting of amplifier 211, and clock recovery 216 which forms the phase-locked-loop required to frame the data acquisition by analog-to-digital converter 210.

Receiver 506 can further include a baseline wander correction circuit 510 that, when combined with adder 515, corrects the output of analog-to-digital converter for signal wander. Baseline wander correction is further described in “Digital Baseline Wander Correction Circuit,” U.S. application Ser. No. 09/151,525, previously incorporated in this disclosure. Receiver 506 can also include A/D reference adjust 517, which adjusts the reference voltage of analog-to-digital converter 210 according to the measured apparent length of the cable associated with transmission channel 201.

Receiver 506 can also include a cable quality and length calculator 518. As described in “Cable Length and Quality Indicator,” U.S. patent application Ser. No. 09/161,346, cable quality and length calculator 518 calculates the length of cable in transmission channel 201 and the quality of transmission channel 201 based on the gain calculation of gain control 215 or the equalizer coefficients of equalizer 511. Both A/D reference 517 and cable quality and length calculation 518 are affected by pre-filter 207, which has the affect of simultaneously making transmission channel 201 appear to be of very high quality and to make the cable length of transmission channel 201 appear longer. The apparent quality increases because pre-filter 207 removes some of the interference caused by transmission channel 201. The cable appears longer if there is any loss of signal strength in pre-filter 207. Cable quality and length calculation 518 can, however, be adjusted for the presence of pre-filter 207 in order to have accurate calculations of cable length and quality.

Receiver 506 can also include an echo canceller 513 and a NEXT canceller 514. NEXT canceller 514 cancels interference on one transmission line based on the transmission of symbols over neighboring lines. Echo canceller 513 cancels interference from symbols transmitted by a transmitter (not shown) associated with receiver 506.

In some transmission systems, signals are transmitted over a cable having multiple wires. Transmission channel 201 and receiver 506 represents detection of the transmitted signal over one of the multiple wires. In which case, signals on neighboring wires affect the transmitted signal on transmission channel 201. NEXT canceller 514 computes the influence of transmitted signal from other pairs of wires at the input of adder 517. The projected influence from symbols transmitted on neighboring lines is subtracted from the digitized symbol with adder 517.

Echo cancelor 513 subtracts the influence of symbols that are reflected back into receiver 506 by transmission along a cable associated with transmission channel 201. In most transceiver systems, receiver 506 and a transmitter (not shown) are coupled to a common host. The transmitter transmits signals through transmission channel 201 to a receiver (not shown) counterpart of transmitter 221. Some of that transmitted signal may be reflected back into receiver 506. Echo cancelor 513 projects the reflected signal based on the transmitted signals and subtracts the influence of that signal at adder 516 and adder 517.

FIG. 5B shows an embodiment of pre-filter 207 that is sensitive to the cable length of transmission channel 201. Pre-filter 207 as shown in FIG. 5B includes pre-filters 510-1 through 510-N. Each of pre-filters 510-1 through 510-N execute transfer functions H_(PF) ¹(ω) through H_(PF) ^(N)(ω), respectively. Each of pre-filters 510-1 through 510-N is optimized to counter the interference from a transmission channel having a particular cable length. Each pre-filter 510-i can be designed by minimizing a cost function such as that shown in Equation 10. Selector 511, in response to the cable length L calculated by cable quality and length calculator 518 (FIG. 5A), selects one of pre-filters 510-1 through 510-N. Selector 512 controls a switch 512 which connects the selected one of pre-filter 510-1 through 510-N with input signal Y_(s)(Ω). Therefore, pre-filter 207 can be selected in order to optimize the performance of receiver 506.

FIG. 5C shows another embodiment of a prefilter 207 according to the present invention. Prefilter 207 of FIG. 5C executes the adaptively controlled transfer function of Equation 13. An input signal Y_(s)(ω) is input to block 515, which executes the transfer function PF(s). Transfer function PF(s) can, for example, be that transfer function described in Equation 14. The input signal Y_(s)(ω) is also input to block 516 which executes the transfer function one. The output signal from block 515 is multiplied by the adaptively chosen parameter V_(c) in multiplier 517 and input to adder 519. The output signal from block 516 is multiplied by 1-V_(c) and added to the output signal from multiplier 517 in adder 519. The output signal from adder 519 is the output signal from prefilter 207, Z_(s)(ω).

FIG. 6A shows a multi-wire receiver 600 according to the present invention. Transmission receiver 600 inputs signals Y_(s) ⁽¹⁾(ω) through Y_(s) ^((M))(ω) from M wires 603-1 through 603-M, respectively. Each of signals Y_(s) ⁽¹⁾(ω) through Y_(s) ^((M))(ω) includes the effects of transmission channel 601, as described above. Additionally, each of the signals also includes effects of cross-talk between wires so that, for example, signal Y_(s) ^((i))(ω), where the i-th wire 603-i is an arbitrary one of wires 603-1 through 603-M, includes a contribution from signals from all of the other wires, i.e. wires 603-1 through 603-(i−1) and wires 603-(i+1) through 603-M.

Individual receivers 602-1 through 602-M receives input signals Y_(s) ⁽¹⁾(ω) through Y_(s) ^((M))(ω), respectively, and outputs signals {α′_(k) ⁽¹⁾} through {α′_(k) ^((M))}, which are input signals to slicers within receivers 602-1 through 602-M, respectively. The symbols determined by receivers 602-1 through 602-M, {{circumflex over (α)}_(k) ⁽¹⁾} through {{circumflex over (α)}_(k) ^((M))}, respectively, are temporary decisions made in order to control the adaptation of parameters within receivers 602-1 through 602-M, respectively. An arbitrary receiver 602-i, which is one of receivers 602-1 through 602-M, also inputs the output symbol streams, {Tx_(k) ⁽¹⁾} through {Tx_(k) ^((M))}, from a transmitter 606 associated with receiver 600. Each of receiver 602-1 through 602-M, then, can include echo cancellation and Near End Cross Talk (NEXT) compensation due to the transmitted symbols of transmitter 606.

In some embodiments, the output symbol streams {α′_(k) ⁽¹⁾} through {α′_(k) ^((M))} are input to a delay skew compensator 604. The output signals from delay skew compensator 604 are input to an M-D decoder 605 for final decision on the received symbols.

Delay Skew Compensator 604 inputs the signals {α′_(k) ⁽¹⁾} through {α′_(k) ^((M))} and aligns the M signals so that any delays between signals received from receivers 602-1 through 602-M, respectively, are removed. Relative delay between signals from each of receivers 602-1 through 602-M may be introduced in transmission channel 601 or by receivers 602-1 through 602-M. The signals from each of receivers 602-1 through 602-M for a particular clock cycle k, {α′_(k) ⁽¹⁾} through {α′_(k) ^((M))}, should arrive at M-D decoder 605 simultaneously.

Decoder 605, then, receives the M signals, one from each of receivers 602-1 through 602-M, respectively, simultaneously. Decoder 605, which may be a Viterbi decoder, then uses these signals to make a final decision on the incoming data. Additionally, decoder 605 may utilize an error detecting code such as that defined in the IEEE standard for gigabit ethernet. See, e.g., IEEE 802.3ab, “Gigabit Long Haul Copper Physical Layer Standards Committee, 1997 Standard. In one embodiment, M-D decoder 604 is a Viterbi decoder which makes a final decision on data which has been encoded by an 8 state Ungerboeck code, as described in the IEEE Gigabit Spec. The Viterbi decoder in this embodiment is a Maximum Likelihood Sequence Estimator, as described in Viterby A. J., “Error bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm,” IEEE Trans. Inf Theory, IT-13, 260-269, April 1967, herein incorporated by reference in its entirety. M-D decoder, therefore, maximizes the probability of correctly estimating the entire sequence of symbols.

FIG. 6B shows an embodiment of receiver 601-i. Receiver 601-i includes an analog prefilter 619 and a digital filter 620. Analog prefilter 619 includes a DC offset adder 610 coupled to a DC offset correction circuit 628, an echo canceller adder 611 coupled to an analog echo canceller circuit 627, an analog multiplier 612 coupled to an analog AGC circuit 220, and analog equalizers 613 and 614 coupled to analog equalizer adaptor circuit 217. Digital filter 620 includes digital equalizer 212, digital echo canceller and NEXT canceller adder 615 coupled to digital echo canceller 620 and NEXT cancellers 618-1 through 618-M without a canceller 618-i, AGC boost 211 coupled to digital AGC circuit 215, baseline wander adder 616 coupled to baseline wander correction circuit 617, and slicer 213. Analog portion 619 is coupled to digital portion 620 through analog-to-digital converter (ADC) 210. For example purposes, slicer 213 is shown as a PAM-5 decoder. A timing recovery loop (clock recovery) 216 controls a clock used in both the analog and digital portion of receiver 601-i and calculates the timing phase parameter τ_(k) ^((i)).

Slicer 213 provides a temporary decision on a symbol stream for wire 601-i, {circumflex over (α)} _(k) ^((i)), and error e_(k) ^((i)) based on an input signal α′_(k) ^((i)), where e_(k) ^((i)) is defined as

e _(k) ^((i))=α′_(k) ^((i))−{circumflex over (α)}_(k) ^((i)).   (25)

The temporary decision â_(k) ^((i)) and error e_(k) ^((i)) are utilized in various circuit loops in receiver 601-i in order to adapt parameters in receiver 601-i.

DC offset correction circuit 628 includes an ADCO control 633 coupled to a digital to analog (DAC) converter 634. DAC 634 provides a signal which is added to the received signal, Y_(s) ^((i))(ω), in DC offset adder 610. ADC control 633 inputs the output signal α_(k) ^((i)) from ADCO 210 and estimates the DC Offset that occurs in analog prefilter 619. This calculated DC Offset is then subtracted from the input signal Y_(s) ^((i))(ω) in adder 610.

Analog echo canceller circuit 627 includes AEC control 629, DACs 630 and 631, and RC circuit 632. AEC control 629 inputs the error signal e_(k) ^((i)) as well as the transmitted signals on wire 603-i (FIG. 6A), {Tx_(k) ^((i))}, and adapts the resistance R_(k) ^((i)) and capacitance C_(k) ^((i)) in an RC circuit 632. Transmit signal TX_(k) ^((i)) is filtered in RC circuit 632 and subtracted from input signal Y_(s) ^((i))(ω) by echo adder 611. The parameters R_(k) ^((i)) and C_(k) ^((i)) are adapted to approximately duplicate the effects of the transmit signal Tx_(k) ^((i)) on the signal input to adder 611. Appropriate values for R and C will minimize the residual echo from the transmit signal TX_(k) ^((i)), which results in minimizing the requirements of digital echo canceller circuit 620. Furthermore, by minimizing the residual echo, analog AGC 220 can provide for maximum boost to input signal Y_(s) ^((i))(ω) through multiplier 612 without overloading ADC 210, which results in clipping. The additional boost at multiplier 612 results in a lessened need for amplification at digital AGC boost 211, minimizing quantization noise.

As previously described, analog gain control circuit 220 outputs a gain signal to multiplier 612 that adjusts the output levels of prefliter 612 to optimize the functionality of ADC 210. FIGS. 6C and 6D show embodiments of analog gain control circuit 220.

One embodiment of an AGC control circuit 625 is shown in FIG. 6C. Test block 630 compares α_(k) ^((i)) with threshold TH_(AGC) and calculates, for each receiver 601-i, α _(k,1) according to equation 20. The value α_(k,2) is calculated according to Equation 21. The value of PD_(AGC) is calculated according to Equation 19 in adder 631. The value of PD_(AGC) is input to an adder 632 and then to saturation block 633. Saturation block 633 saturates at, for example, 13 bits. The output from saturation block 633 is delayed one clock cycle and added to PD_(AGC) at adder 632. The combination of adder 632, saturation block 633, and delay 635 forms an accumulator.

The output of saturation block 633 is right shifted by a particular number of bits, for example 7 bits, in shifter 634 to give an output of a particular number of bits, for example 6 bits. The output signal from shifter 634 provides an input signal to DAC 626. The analog output signal from DAC 626, which is the output signal from analog AGC control circuit 220 (FIG. 6B), is multiplied by the input signal Y_(s) ^((i))(ω) in multiplier 612.

Because of the low frequency nature the input to DAC 626 of AGC 220 will have very small variations from sample to sample. In most cases, the variation is at most one count. FIG. 6D shows an embodiment of analog AGC control circuit 220 (AGC control 625 and DAC 626) that takes advantage of this feature. Instead of a “general purpose” 6 bit D/A, a less expensive Sigma-Delta D/A could be used for DAC 626. In that case, saturation block 633 is replaced with an input to a smaller block 636 of size, for example, 7 bits. The ACC value, the output signal from the accumulator formed by adder 632, block 636 and delay 635, is wrapped around (modulo) to a particular number of bits, for example 7 bits. The output of block 636 is a three-level signal representing overflow, no change, or underflow of the accumulation value. The three-level signal is the output signal received by the Sigma-Delta DAC 626. DAC 626, then, outputs an analog value which is multiplied by the input signal Y_(s) ^((i))(ω) in multiplier 612.

In the embodiment shown in FIG. 6B, the analog equalization is accomplished by analog equalizer 613 cascaded with analog equalizer 614. Each of analog equalizer 613 and analog equalizer 614 is controlled by analog equalizer control circuit 217. Analog equalizer control circuit 217 includes AEQ control 622 coupled to DAC 623, which is coupled to control analog equalizer 613, and coupled to DAC 624, which is coupled to control analog equalizer 614. Analog equalizers 613 and 614 accomplish partial equalization in the input signal Y_(s) ^((i))(ω), resulting in a lessened requirement for digital equalization. Analog equalizers and analog equalization control circuit 217 operate as is described above with Equations 14 through 18.

ADC 210 receives the output signal Z_(s) ^((i))(ω) from analog prefilter 619 and digitizes the signal. The output from ADC 210 is α_(k) ^((i)).

ADC 210 samples input signal Z_(s) ^((i))(ω) based upon the clock output from timing recover loop (clock recovery) 216 and phase τ_(k) ^((i)). Clock recovery 216 recovers the frequency of the received signal (i.e., the frequency of transmitter 221 (FIG. 2)) and finds the optimal timing phase τ_(k) ^((i)) of the incoming signal. For a constant clock frequency offset between the remote transmitter's digital-to-analog converter and analog to digital converter 210, the optimal timing phase τ varies linearly with time. The rate of change of τ_(k) ^((i)) is proportional to the clock frequency offset.

Clock recovery 216 can be second order loop. One embodiment of clock recovery 216 is shown in FIG. 6E. A phase detector 650 estimates the difference between the optimal phase and the current value of τ_(k) ^((i)) based on the output symbol â_(k) ^((i)) and the error calculation e_(k) ^((i)). The output signal from phase detector 650, PD_(CR) for recevier 601-i, can be determined in several manners, including a slope method and a Mueller & Mueller (M&M) method. In the M&M method, the output signal from the phase detector is

PD _(CR) =e _(k−1) ^((i)){circumflex over (α)}_(k) ^((i)) −e _(k) ^((i)){circumflex over (α)}_(k−1) ^((i)).   (26)

In the slope method,

PD _(CR) =e _(k) ^((i))slope(k),   (27)

where

$\begin{matrix} {{{slope}(k)} = \left( \begin{matrix} {1,} & {{{if}\mspace{14mu} {\hat{a}}_{k - 1}^{(i)}} < {\hat{a}}_{k}^{(i)} < {\hat{a}}_{k + 1}^{(i)}} \\ {{- 1},} & {{{if}\mspace{14mu} {\hat{a}}_{k - 1}^{(i)}} > {\hat{a}}_{k}^{(i)} > {\hat{a}}_{k + 1}^{(i)}} \\ {0,} & {{otherwise}.} \end{matrix} \right.} & (28) \end{matrix}$

The output signal from the phase detector, PD_(CR), is input to a loop filter 651 that has a proportional and an integral part. The output signal from loop filter 651, indicating the correction on the clock frequency, is input to a frequency controlled oscillator 652 which causes ADC 210 to sample at an optimal phase by controlling the sampling frequency of the ADC. Frequency controlled oscillator 652, in other words, outputs a clock signal whose zero-crossings are given by NT+τ_(k) ^((i)).

If the coefficient c⁻¹ of digital equalizer 212 is adapted, then the adaptation algorithms between adapter 214 and clock recover 216 will interact adversely, often causing failure of the receiver. To prevent this interaction, c⁻¹ is fixed, for example at −⅛, in order that the timing loop can converge to an optimum phase.

Since part of the equalization is accomplished in analog equalizers 613 and 614, digital equalizer 212 can be simplified. For example, digital equalizer 212 can be a linear equalizer without causing large amounts of noise enhancement. Of course, as has been previously discussed, in other embodiments digital equalizer 212 can be any equalization scheme.

High frequency signals are attenuated more by transmission channel 601 than are low frequency signals. The equalization, between analog equalizers 613 and 614 and digital equalizer 212, then should equalize the attenuation difference across the frequency band.

In one embodiment, digital equalizer 212 is a linear equalizer executing the transfer function

H _(EQ) ^((i)) =c _(k,−1) ^((i)) z+c _(k,0) ^((i)) +c _(k,1) ^((i)) z ⁻¹ + . . . +c _(k,K) ^((i)) z ^(−K).   (29)

The parameter K can be any positive integer, for example K=1 in some embodiments. The parameter c_(k,−1) can be fixed, for example at −⅛, to avoid interaction with the adaptation performed by timing recovery loop 216. Further, the parameter c_(k,0) can be fixed, for example at 1, to avoid interaction with digital AGC 215. The remaining equalizer parameters, c_(k,1) through c_(k,K) are adaptively chosen by coefficient update 214. Coefficient update 214 can use a least mean square (LMS) technique to continuously adjust the equalizer parameters such that

c _(k+1,j) ^((i)) =c _(k,j) ^((i))−μ_(EQ,j) ^((i)) sign(α_(k) ^((i)))e _(k) ^((i)).   (30)

The LMS technique minimizes the mean square error, which is a function of intersymbol interference and random noise, of the input signal at slicer 213. The parameter μ_(EQ,j) ^((i)) controls the rate at which c_(k,j) ^((i)) changes. In some embodiments, μ_(EQ,j) ^((i)) is set to about 10⁻³ on chip powerup and reduced to about 10⁻⁵ for continuous operation.

After equalization with digital equalizer 212, digital echo canceller 620 removes the residual echo due to transmitter 606 transmitting on wire 603-i which is left by analog echo cancellor circuit 627. NEXT cancellers 618-1 through 618-M removes the near end cross talk (NEXT) from transmitter 606 on wires 603-1 through 603-M, respectively, other than wire 603-i. In a four-wire system (M=4), there are three NEXT cancellors 603-1 through 603-M except for 603-i and one echo cancellor for signals transmitted on wire 603-i.

Digital echo canceller 620 cancels the residual echo not cancelled by analog echo cancellor circuit 627. The bulk of the echo cancellation is accomplished by analog echo cancellor circuit 627. Removing the residual echo in digital echo canceller 620 necessary to achieve the bit-error rate (BER) performance of receiver 602-i.

In one embodiment, echo canceller 620 uses a finite-impulse response (FIR) to estimate the residual echo on the channel. FIR echo canceller 620 executes a transfer function given by

$\begin{matrix} {{{EC}_{k}^{(i)} = {\sum\limits_{p = 0}^{L}\; {ϛ_{k,p}^{(i)}z^{- p}}}},} & (31) \end{matrix}$

where L is an integer, for example L=64 or L−56. Echo canceller 620 inputs the transmitted symbol stream {Tx_(k) ^((i))} and estimates the residual echo at that point in the data path, including the impulse response of the residual echo channel after analog echo canceller 627, analog AGC 625, analog equalizers 613 and 614, and digital equalizer 212. Each of the parameters in Equation 31, ζ_(k,p) ^((i)), are chosen by an adaption loop using a least mean squares technique, i.e.

ζ_(k+1,j) ^((i))=ζ_(k,j) ^((i))−μ_(EC,j) ^((i)) sign(Tx _(k−j) ^((i)))e _(k) ^((i)),   (32)

as was previously discussed. The coefficients ζ_(k,j) ^((i)) are continuously adjusted to maintain the minimum mean squared error at slicer 213. Again, the parameter μ_(EC,j) ^((i)) may initially be set high (e.g. 10⁻³) and then lowered (e.g. 10⁻⁵) for continuous operation.

NEXT cancellers 618-1 through 618-M cancel the near end cross talk which is a result of transmitter 606 transmitting on wires 603-1 through 603-M. Note that there is no NEXT canceller 618-i for receiver 601-i because the effects of transmitting symbols on wire 603-i is cancelled by analog echo canceller 627 and digital echo canceller 620. Each of NEXT cancellers 618-1 through 618-M estimates the impulse response from the NEXT in a FIR block. The impulse response that is used to estimate the NEXT at this point in the data path is the impulse response of the NEXT contribution in transmission channel 601 that has been added to the receive signal filtered by analog prefilter 619 and digital equalizer 212. Each of NEXT canceller 618-1 through 618-M executes a transfer function given by

$\begin{matrix} {{{NE}_{p,k}^{(i)} = {\sum\limits_{l = 0}^{L}\; {\xi_{p,k,l}^{(i)}z^{- l}}}},} & (33) \end{matrix}$

where p denotes a channel that is not channel i and L can be any positive integer, for example L=44 or L=16. Each of the coefficients ξ_(p,k,l) ^((i)) is adaptively chosen in a least mean squares technique, i.e.

ξ_(p,k+1,l) ^((i))=ξ_(p,k,l) ^((i))+μ_(NE,p,l) ^((i)) sign(Tx _(p,k−1))e _(k) ^((i)).   (34)

The coefficients are continuously updated to maintain the minimum mean squared error at slicer 213. The parameter μ_(NE,p,l) ^((i)) may initially be set high (e.g. ˜10⁻³) and the lowered (e.g. ˜10⁻⁵) for steady operation.

The NEXT and ECHO estimations performed by Echo canceller 620 and NEXT cancellers 618-1 through 618-M are subtracted from the output signal of equalizer 212 in adder 615.

Digital AGC 215 inputs a gain signal g_(k) ^((i)) to AGC boost 211 which digitally amplifies the output signal from adder 615. The signal is boosted by AGC boost 211 to levels determined by slicer 213. The gain to AGC boost 211 is determined by digital AGC 215. The gain g_(k) ^((i)) is set to counter the losses resulting from transmission channel 601 and not recovered in analog prefilter 619. During acquisition, the gain g_(k) ^((i)) can be updated by the equation

g _(k+1) ^((i)) =g _(k) ^((i))−μ_(AGC) ^((i))(e _(non,k) ^((i))),   (35)

where TH_(AGC) ^((i)) is the average absolute value of α′_(k) ^((i)) and

e _(non,k) ^((i))=|α′_(k) ^((i)) |−TH _(AGC) ^((i)).   (36)

The parameter μ_(AGC) ^((i)) can initially be set high and then lowered during steady state operation. During steady operation, a least means square approach can be taken, in which case

g _(k+1) ^((i)) =g _(k) ^((i))−μ_(AGC) ^((i)) sign({circumflex over (α)}_(k) ^((i)))e _(k) ^((i)).   (37)

Finally, baseline wander circuit 617 corrects for baseline wander. A discussion of baseline wander can be found in U.S. patent application Ser. No. 09/151,525, previously incorporated by reference.

One skilled in the art will recognize that the components of receiver 506 may be arranged differently. For example, in FIG. 6B amplifier 211 follows equalizer 212 while in FIG. 2A equalizer 212 follows amplifer 211. One skilled in the art will also recognize that receivers according to the present invention may not have some of the features shown in FIGS. 2A, 5A, and 6B or, alternatively, may have other features not shown in FIGS. 2A, 5A, and 6B. FIGS. 2A, 5A, and 6B, therefore, are not exhaustive of all configurations of receivers that are nonetheless within the scope of this disclosure.

The above examples, therefore, are demonstrative only. One skilled in the art can recognize obvious variations which fall within the scope of this invention. As such, the invention is limited only by the following claims. 

1-35. (canceled)
 36. A transceiver system comprising (a) a primary transmitter for providing a primary symbol-information-carrying output signal and (b) a primary receiver for receiving a primary symbol-information-carrying input analog signal that includes an echo of the output signal, the receiver comprising: analog echo-cancelling circuitry for operating on the input analog signal, or on a first intermediate analog signal generated from the input analog signal, to produce an echo-reduced analog signal in which the echo is reduced; an analog-to-digital converter for converting the echo-reduced analog signal, or a second intermediate analog signal generated from the echo-reduced analog signal, into an initial digital signal; digital echo-cancelling circuitry for adaptively operating on the initial digital signal, or on a first intermediate digital signal generated from the initial digital signal, to produce an echo-reduced digital signal in which the echo is further reduced; and an output decoder for decoding the echo-reduced digital signal, or a second intermediate digital signal generated from the echo-reduced digital signal, into a stream of symbols, the digital echo-cancelling circuitry having echo-filtering characteristics that are adaptively adjustable in response to information provided by operating on the echo-reduced digital signal or on a further digital signal generated from the echo-reduced digital signal.
 37. A transceiver system as in claim 36 wherein the information for adaptively adjusting the echo-filtering characteristics of the digital echo-cancelling circuitry comprises an error signal generated by decoding the echo-reduced or further digital signal.
 38. A transceiver system as in claim 37 wherein the error signal varies at any time during operation of the receiver according to the difference between (i) the echo-reduced or further digital signal at that time and (ii) a corresponding one of an alphabet of predefined symbols from which the stream of symbols is substantially formed, the corresponding predefined symbol being produced by decoding the echo-reduced or further digital signal at that time.
 39. A transceiver system comprising (a) a primary transmitter for providing a primary symbol-information-carrying output signal and (b) a primary receiver for receiving a primary symbol-information-carrying input analog signal that includes an echo of the output signal, the receiver comprising: analog echo-cancelling circuitry for operating on the input analog signal, or on a first intermediate analog signal generated from the input analog signal, to produce an echo-reduced analog signal in which the echo is reduced; an analog-to-digital converter for converting the echo-reduced analog signal, or a second intermediate analog signal generated from the echo-reduced analog signal, into an initial digital signal; digital echo-cancelling circuitry for adaptively operating on the initial digital signal, or on a first intermediate digital signal generated from the initial digital signal, to produce an echo-reduced digital signal in which the echo is further reduced; and an output decoder for decoding the echo-reduced digital signal, or a second intermediate digital signal generated from the echo-reduced digital signal, into a stream of symbols, the digital echo-cancelling circuitry having echo-filtering characteristics that are adaptively adjustable in response to information provided by operating on the echo-reduced digital signal or on a further digital signal generated from the echo-reduced digital signal, the information for adaptively adjusting the echo-filtering characteristics of the digital echo-cancelling circuitry comprising an error signal generated by decoding the echo-reduced or further digital signal, the error signal varying at any time during operation of the receiver according to the difference between (i) the echo-reduced or further digital signal at that time and (ii) a corresponding one of an alphabet of predefined symbols from which the stream of symbols is substantially formed, the corresponding predefined symbol being produced by decoding the echo-reduced or further digital signal at that time, the predefined symbols used in generating the error signal being generated along a different signal processing path than the stream of symbols.
 40. A transceiver system as in claim 37 wherein the further digital signal substantially constitutes the second intermediate digital signal.
 41. A transceiver system as in claim 37 wherein the digital echo-cancelling circuitry comprises: an echo filter responsive to the error and output signals for generating an echo-estimate digital signal; and an adding/subtracting element for generating the echo-reduced digital signal by substantially subtracting the echo-estimate digital signal from the initial or first intermediate digital signal.
 42. A transceiver system as in claim 41 wherein the echo filter comprises echo filtering circuitry that operates substantially according to a transfer function $\sum\limits_{j = 0}^{L}\; {ϛ_{k,j}z^{- j}}$ where z is a time-related variable, j is a general running integer, k is a time-index integer, ζ_(k,j) is an adaptable jth coefficient at the kth time index, and L is a selected positive integer.
 43. A transceiver system comprising (a) a primary transmitter for providing a primary symbol-information-carrying output signal and (b) a primary receiver for receiving a primary symbol-information-carrying input analog signal that includes an echo of the output signal, the receiver comprising: analog echo-cancelling circuitry for operating on the input analog signal, or on a first intermediate analog signal generated from the input analog signal, to produce an echo-reduced analog signal in which the echo is reduced; an analog-to-digital converter for converting the echo-reduced analog signal, or a second intermediate analog signal generated from the echo-reduced analog signal, into an initial digital signal; digital echo-cancelling circuitry for adaptively operating on the initial digital signal, or on a first intermediate digital signal generated from the initial digital signal, to produce an echo-reduced digital signal in which the echo is further reduced; and an output decoder for decoding the echo-reduced digital signal, or a second intermediate digital signal generated from the echo-reduced digital signal, into a stream of symbols, the digital echo-cancelling circuitry having echo-filtering characteristics that are adaptively adjustable in response to information provided by operating on the echo-reduced digital signal or on a further digital signal generated from the echo-reduced digital signal, the information for adaptively adjusting the echo-filtering characteristics of the digital echo-cancelling circuitry comprising an error signal generated by decoding the echo-reduced or further digital signal, the digital echo-cancelling circuitry comprising (i) an echo filter responsive to the error and output signals for generating an echo-estimate digital signal and (ii) an adding/subtracting element for generating the echo-reduced digital signal by substantially subtracting the echo-estimate digital signal from the initial or first intermediate digital signal, the echo filter comprises echo filtering circuitry that operates substantially according to a transfer function $\sum\limits_{j = 0}^{L}{ϛ_{k,j}z^{- j}}$ where z is a time-related variable, j is a general running integer, k is a time-index integer, ζ_(k,j) is an adaptable jth coefficient at the kth time index, and L is a selected positive integer, the echo filter adaptively updating coefficients ζ_(k,j) substantially according to: ζ_(k+1,j)=ζ_(k,j)−μ_(EC,j) sign(Tx _(k−j))e _(k) where μ_(EC,j) is an adjustment parameter for the jth coefficient ζ_(k,j), sign (Tx_(k−j)) is the algebraic sign of the value of the output signal at the (k-j)th time period, and e_(k) is the value of the error signal.
 44. A transceiver system as in claim 43 wherein the echo filter continuously updates coefficients ζ_(k,j) to substantially minimize the mean squared value of the error signal.
 45. A transceiver system as in claim 36 wherein the analog echo-cancelling circuitry operates adaptively to reduce effects of the echo in the input or first intermediate analog signal.
 46. A method comprising: transmitting a primary symbol-information-carrying output signal; receiving a primary symbol-information-carrying input analog signal that includes an echo of the output signal; operating on the input analog signal, or on a first intermediate analog signal generated from the input analog signal, to produce an echo-reduced analog signal in which the echo is reduced; converting the echo-reduced analog signal, or a second intermediate analog signal generated from the echo-reduced analog signal, into an initial digital signal; adaptively operating on the initial digital signal, or on a first intermediate digital signal generated from the initial digital signal, to produce an echo-reduced digital signal in which the echo is further reduced; decoding the echo-reduced digital signal, or a second intermediate digital signal generated from the echo-reduced digital signal, into a stream of symbols; and, during conversion of the input analog signal into the stream of symbols, operating on the echo-reduced digital signal, or on a further digital signal generated from the echo-reduced digital signal, to provide information for adaptively adjusting echo-filtering characteristics used in the adaptively operating act to produce the echo-reduced digital signal.
 47. A method as in claim 46 wherein the act of operating on the echo-reduced or further digital signal comprises generating an error signal by decoding the echo-reduced or further digital signal.
 48. A method as in claim 47 wherein the error signal varies at any time during the method according to the difference between (i) the echo-reduced or further digital signal at that time and (ii) a corresponding one of an alphabet of predefined symbols from which the stream of symbols is substantially formed, the corresponding predefined symbol being produced by decoding the echo-reduced or further digital signal at that time.
 49. A method comprising: transmitting a primary symbol-information-carrying output signal; receiving a primary symbol-information-carrying input analog signal that includes an echo of the output signal; operating on the input analog signal, or on a first intermediate analog signal generated from the input analog signal, to produce an echo-reduced analog signal in which the echo is reduced; converting the echo-reduced analog signal, or a second intermediate analog signal generated from the echo-reduced analog signal, into an initial digital signal; adaptively operating on the initial digital signal, or on a first intermediate digital signal generated from the initial digital signal, to produce an echo-reduced digital signal in which the echo is further reduced; decoding the echo-reduced digital signal, or a second intermediate digital signal generated from the echo-reduced digital signal, into a stream of symbols; and, during conversion of the input analog signal into the stream of symbols, operating on the echo-reduced digital signal, or on a further digital signal generated from the echo-reduced digital signal, to provide information for adaptively adjusting echo-filtering characteristics used in the adaptively operating act to produce the echo-reduced digital signal, the act of operating on the echo-reduced or further digital signal comprising generating an error signal by decoding the echo-reduced or further digital signal, the error signal varies at any time during the method according to the difference between (i) the echo-reduced or further digital signal at that time and (ii) a corresponding one of an alphabet of predefined symbols from which the stream of symbols is substantially formed, the corresponding predefined symbol being produced by decoding the echo-reduced or further digital signal at that time, the decoding to produce the predefined symbols used in generating the error signal being performed along a different signal processing path than the decoding to generate the stream of symbols.
 50. A transceiver system as in claim 36 further including (a) an additional transmitter for providing an additional symbol-information-carrying output signal and (b) an additional receiver for receiving an additional symbol-information-carrying input analog signal, the primary receiver further including crosstalk-cancelling circuitry for causing the stream of symbols to be produced with reduced effects of crosstalk from the additional output signal.
 51. A transceiver system as in claim 50 wherein the crosstalk-cancelling circuitry comprises: a crosstalk filter responsive to the error and additional output signals for generating a crosstalk-estimate digital signal; and an adding/subtracting element for generating a crosstalk-reduced digital signal by substantially subtracting the crosstalk-estimate digital signal from the initial digital signal or from a crosstalk-cancellation intermediate digital signal generated from the initial digital signal.
 52. A transceiver system as in claim 51 wherein the crosstalk filter comprises crosstalk filtering circuitry that operates substantially according to a transfer function $\sum\limits_{j = 0}^{L}{\xi_{p,k,j}z^{- j}}$ where z is a time-related variable, j is a general running integer, k is a time-index integer, p is an integer representing a channel carrying the additional output signal, ξ_(p,k,j) is an adaptable jth coefficient at the kth time index for the channel carrying the additional output signal, and L is a selected positive integer.
 53. A transceiver system comprising (a) a primary transmitter for providing a primary symbol-information-carrying output signal, (b) a primary receiver for receiving a primary symbol-information-carrying input analog signal that includes an echo of the output signal, (c) an additional transmitter for providing an additional symbol-information-carrying output signal, and (d) an additional receiver for receiving an additional symbol-information-carrying input analog signal, the primary receiver comprising: analog echo-cancelling circuitry for operating on the input analog signal, or on a first intermediate analog signal generated from the input analog signal, to produce an echo-reduced analog signal in which the echo is reduced; an analog-to-digital converter for converting the echo-reduced analog signal, or a second intermediate analog signal generated from the echo-reduced analog signal, into an initial digital signal; digital echo-cancelling circuitry for adaptively operating on the initial digital signal, or on a first intermediate digital signal generated from the initial digital signal, to produce an echo-reduced digital signal in which the echo is further reduced; an output decoder for decoding the echo-reduced digital signal, or a second intermediate digital signal generated from the echo-reduced digital signal, into a stream of symbols, the digital echo-cancelling circuitry having echo-filtering characteristics that are adaptively adjustable in response to information provided by operating on the echo-reduced digital signal or on a further digital signal generated from the echo-reduced digital signal; and crosstalk-cancelling circuitry for causing the stream of symbols to be produced with reduced effects of crosstalk from the additional output signal, the crosstalk-cancelling circuitry comprising (i) a crosstalk filter responsive to the error and additional output signals for generating a crosstalk-estimate digital signal and (ii) an adding/subtracting element for generating a crosstalk-reduced digital signal by substantially subtracting the crosstalk-estimate digital signal from the initial digital signal or from a crosstalk-cancellation intermediate digital signal generated from the initial digital signal, the crosstalk filter comprises crosstalk filtering circuitry that operates substantially according to a transfer function $\sum\limits_{j = 0}^{L}{\xi_{p,k,j}z^{- j}}$ where z is a time-related variable, j is a general running integer, k is a time-index integer, p is an integer representing a channel carrying the additional output signal, ξ_(p,k,j) is an adaptable jth coefficient at the kth time index for the channel carrying the additional output signal, and L is a selected positive integer, the crosstalk filter adaptively updating coefficients ξ_(p,k,j) substantially according to: ξ_(p,k+1,j)=ξ_(p,k,j)+μ_(NE,) _(p,j) sign(Tx_(k-j) ^((p)))e_(k) where μ_(NE,) _(p,j) is an adjustment parameter for the jth coefficient ξ_(p,k,j), sign(Tx_(k-j) ^((p))) is the algebraic sign of the value of the additional output signal at the (k-j)th time period, and e_(k) is the value of the error signal.
 54. A transceiver system as in claim 53 wherein the crosstalk filter continuously updates coefficients ξ_(p,k,j) to substantially minimize the mean squared value of the error signal.
 55. A transceiver system as in claim 51 wherein the digital echo-cancelling circuitry comprises: an echo filter responsive to the error and output signals for generating an echo-estimate digital signal; and an adding/subtracting element for generating the echo-reduced digital signal by substantially subtracting the echo-estimate digital signal from the initial or first intermediate digital signal.
 56. A transceiver system as in claim 55 wherein: the adding/subtracting element in the digital echo-cancelling circuitry is substantially the same element as the adding/subtracting element in the crosstalk-cancelling circuitry; and the first intermediate digital signal is substantially the same signal as the crosstalk-cancellation intermediate digital signal such that the echo-reduced digital signal is substantially the same signal as the crosstalk-reduced digital signal.
 57. A transceiver system as in claim 36 wherein the receiver further includes a digital equalizer for adaptively equalizing the initial digital signal, or a third intermediate digital signal generated from the initial digital signal, to produce an equalized digital signal with reduced intersymbol interference.
 58. A transceiver system as in claim 36 wherein the receiver further includes an analog equalizer for adaptively equalizing the input analog signal, or a third intermediate analog signal generated from the input analog signal, to produce an equalized analog signal with reduced intersymbol interference.
 59. A transceiver system as in claim 58 wherein the receiver further includes a digital equalizer for adaptively equalizing the initial digital signal, or a third intermediate digital signal generated from the initial digital signal, to produce an equalized digital signal with further reduced intersymbol interference.
 60. A transceiver system comprising (a) a primary transmitter for providing a primary symbol-information-carrying output signal and (b) a primary receiver for receiving a primary symbol-information-carrying input analog signal that includes an echo of the output signal, the receiver comprising: analog echo-cancelling circuitry for adaptively operating on the input analog signal, or on a first intermediate analog signal generated from the input analog signal, to produce an echo-reduced analog signal in which the echo is reduced; an analog-to-digital converter for converting the echo-reduced analog signal, or a second intermediate analog signal generated from the echo-reduced analog signal, into an initial digital signal; digital echo-cancelling circuitry for adaptively operating on the initial digital signal, or on a first intermediate digital signal generated from the initial digital signal, to produce an echo-reduced digital signal in which the echo is further reduced; and an output decoder for decoding the echo-reduced digital signal, or a second intermediate digital signal generated from the echo-reduced digital signal, into a stream of symbols, the echo-cancelling circuitries having echo-filtering characteristics that are adaptively adjustable during conversion of the input analog signal into the stream of symbols.
 61. A transceiver system as in claim 60 wherein the digital echo-cancelling circuitry adaptively adjusts its echo-filtering characteristics in response to information provided by operating on the echo-reduced digital signal or on a further digital signal generated from the echo-reduced digital signal.
 62. A transceiver system as in claim 60 wherein the digital echo-cancelling circuitry adaptively adjusts its echo-filtering characteristics in response to an error signal generated by decoding the echo-reduced digital signal or a further digital signal generated from the echo-reduced digital signal.
 63. A transceiver system as in claim 62 wherein the error signal varies at any time during operation of the receiver according to the difference between (i) the echo-reduced or further digital signal at that time and (ii) a corresponding one of an alphabet of predefined symbols from which the stream of symbols is substantially formed, the corresponding predefined symbol being produced by decoding the echo-reduced or further digital signal at that time.
 64. A transceiver system comprising (a) a primary transmitter for providing a primary symbol-information-carrying output signal and (b) a primary receiver for receiving a primary symbol-information-carrying input analog signal that includes an echo of the output signal, the receiver comprising: analog echo-cancelling circuitry for adaptively operating on the input analog signal, or on a first intermediate analog signal generated from the input analog signal, to produce an echo-reduced analog signal in which the echo is reduced; an analog-to-digital converter for converting the echo-reduced analog signal, or a second intermediate analog signal generated from the echo-reduced analog signal, into an initial digital signal; digital echo-cancelling circuitry for adaptively operating on the initial digital signal, or on a first intermediate digital signal generated from the initial digital signal, to produce an echo-reduced digital signal in which the echo is further reduced; and an output decoder for decoding the echo-reduced digital signal, or a second intermediate digital signal generated from the echo-reduced digital signal, into a stream of symbols, the echo-cancelling circuitries having echo-filtering characteristics that are adaptively adjustable during conversion of the input analog signal into the stream of symbols, the digital echo-cancelling circuitry adaptively adjusts its echo-filtering characteristics in response to an error signal generated by decoding the echo-reduced digital signal or a further digital signal generated from the echo-reduced digital signal, the error signal varying at any time during operation of the receiver according to the difference between (i) the echo-reduced or further digital signal at that time and (ii) a corresponding one of an alphabet of predefined symbols from which the stream of symbols is substantially formed, the corresponding predefined symbol being produced by decoding the echo-reduced or further digital signal at that time, the predefined symbols used in generating the error signal being generated along a different signal processing path than the stream of symbols.
 65. A transceiver system as in claim 64 further including an additional decoder for generating the error signal.
 66. A transceiver system as in claim 62 wherein the digital echo-cancelling circuitry comprises; an echo filter responsive to the error and output signals for generating an echo-estimate digital signal; and an adding/subtracting element for generating the echo-reduced digital signal by substantially subtracting the echo-estimate digital signal from the initial or first intermediate digital signal.
 67. A transceiver system as in claim 66 wherein the echo filter comprises echo filtering circuitry that operates substantially according to a transfer function $\sum\limits_{j = 0}^{L}{ϛ_{k,j}z^{- j}}$ where z is a time-related variable, j is a general running integer, k is a time-index integer, ζ_(k,j) is an adaptable jth coefficient at the kth time index, and L is a selected positive integer.
 68. A transceiver system comprising (a) a primary transmitter for providing a primary symbol-information-carrying output signal and (b) a primary receiver for receiving a primary symbol-information-carrying input analog signal that includes an echo of the output signal, the receiver comprising: analog echo-cancelling circuitry for adaptively operating on the input analog signal, or on a first intermediate analog signal generated from the input analog signal, to produce an echo-reduced analog signal in which the echo is reduced; an analog-to-digital converter for converting the echo-reduced analog signal, or a second intermediate analog signal generated from the echo-reduced analog signal, into an initial digital signal; digital echo-cancelling circuitry for adaptively operating on the initial digital signal, or on a first intermediate digital signal generated from the initial digital signal, to produce an echo-reduced digital signal in which the echo is further reduced; and an output decoder for decoding the echo-reduced digital signal, or a second intermediate digital signal generated from the echo-reduced digital signal, into a stream of symbols, the echo-cancelling circuitries having echo-filtering characteristics that are adaptively adjustable during conversion of the input analog signal into the stream of symbols, the digital echo-cancelling circuitry adaptively adjusting its echo-filtering characteristics in response to an error signal generated by decoding the echo-reduced digital signal or a further digital signal generated from the echo-reduced digital signal, the digital echo-cancelling circuitry comprising (i) an echo filter responsive to the error and output signals for generating an echo-estimate digital signal and (ii) an adding/subtracting element for generating the echo-reduced digital signal by substantially subtracting the echo-estimate digital signal from the initial or first intermediate digital signal, the echo filter comprising echo filtering circuitry that operates substantially according to a transfer function $\sum\limits_{j = 0}^{L}{ϛ_{k,j}z^{- j}}$ where z is a time-related variable, j is a general running integer, k is a time-index integer, ζ_(k,j) is an adaptable jth coefficient at the kth time index, and L is a selected positive integer, the echo filter adaptively updating coefficients ζ_(k,j) substantially according to: ζ_(k+1,j)=ζ_(k,j)−μ_(EC,) _(j) sign(Tx_(k-j)e) _(k) where μEC _(j) is an adjustment parameter for the jth coefficient ζ_(k,j), sign (Tx_(k-j)) is the algebraic sign of the value of the output signal at the (k-j)th time period, and e_(k) is the value of the error signal.
 69. A transceiver system as in claim 68 wherein the echo filter continuously updates coefficients ζ_(k,j) to substantially minimize the mean squared value of the error signal.
 70. A transceiver system as in claim 60 further including (a) an additional transmitter for providing an additional symbol-information-carrying output signal and (b) an additional receiver for receiving an additional symbol-information-carrying input analog signal, the primary receiver further including crosstalk-cancelling circuitry for causing the stream of symbols to be produced with reduced effects of crosstalk from the additional output signal.
 71. A transceiver system as in claim 70 wherein the crosstalk-cancelling circuitry comprises: a crosstalk filter responsive to the error and additional output signals for generating a crosstalk-estimate digital signal; and an adding/subtracting element for generating a crosstalk-reduced digital signal by substantially subtracting the crosstalk-estimate digital signal from the initial digital signal or from a crosstalk-cancellation intermediate digital signal generated from the initial digital signal.
 72. A transceiver system as in claim 71 wherein the crosstalk filter comprises crosstalk filtering circuitry that operates substantially according to a transfer function $\sum\limits_{j = 0}^{L}{\xi_{p,k,j}z^{- j}}$ where z is a time-related variable, j is a general running integer, k is a time-index integer, p is an integer representing a channel carrying the additional output signal, ξ_(p,k,j) is an adaptable jth coefficient at the kth time index for the channel carrying the additional output signal, and L is a selected positive integer.
 73. A transceiver system comprising (a) a primary transmitter for providing a primary symbol-information-carrying output signal, (b) a primary receiver for receiving a primary symbol-information-carrying input analog signal that includes an echo of the output signal, (c) an additional transmitter for providing an additional symbol-information-carrying output signal, and (d) an additional receiver for receiving an additional symbol-information-carrying input analog signal, the primary receiver comprising: analog echo-cancelling circuitry for adaptively operating on the input analog signal, or on a first intermediate analog signal generated from the input analog signal, to produce an echo-reduced analog signal in which the echo is reduced; an analog-to-digital converter for converting the echo-reduced analog signal, or a second intermediate analog signal generated from the echo-reduced analog signal, into an initial digital signal; digital echo-cancelling circuitry for adaptively operating on the initial digital signal, or on a first intermediate digital signal generated from the initial digital signal, to produce an echo-reduced digital signal in which the echo is further reduced; an output decoder for decoding the echo-reduced digital signal, or a second intermediate digital signal generated from the echo-reduced digital signal, into a stream of symbols, the echo-cancelling circuitries having echo-filtering characteristics that are adaptively adjustable during conversion of the input analog signal into the stream of symbols; and crosstalk-cancelling circuitry for causing the stream of symbols to be produced with reduced effects of crosstalk from the additional output signal, the crosstalk-cancelling circuitry comprising (i) a crosstalk filter responsive to the error and additional output signals for generating a crosstalk-estimate digital signal and (ii) an adding/subtracting element for generating a crosstalk-reduced digital signal by substantially subtracting the crosstalk-estimate digital signal from the initial digital signal or from a crosstalk-cancellation intermediate digital signal generated from the initial digital signal, the crosstalk filter comprising crosstalk filtering circuitry that operates substantially according to a transfer function $\sum\limits_{j = 0}^{L}{\xi_{p,k,j}z^{- j}}$ where z is a time-related variable, j is a general running integer, k is a time-index integer, p is an integer representing a channel carrying the additional output signal, ξ_(p,k,j) is an adaptable jth coefficient at the kth time index for the channel carrying the additional output signal, and L is a selected positive integer, the crosstalk filter adaptively updating coefficients ξ_(p,k,j) substantially according to: ξ_(p,k+1,j)=ξ_(p,k,j)+μ_(NE,p,j)sign(Tx_(k-j) ^((p)))e_(k) where μ_(NE,p,j) is an adjustment parameter for the jth coefficient ξ_(p,k,j), sign(Tx_(k-j) ^((p))) is the algebraic sign of the value of the additional output signal at the (k-j)th time period, and e_(k) is the value of the error signal.
 74. A transceiver system as in claim 73 wherein the crosstalk filter continuously updates coefficients ξ_(p,k,j) to substantially minimize the mean squared value of the error signal.
 75. A transceiver system as in claim 71 wherein the digital echo-cancelling circuitry comprises: an echo filter responsive to the error and output signals for generating an echo-estimate digital signal; and an adding/subtracting element for generating the echo-reduced digital signal by substantially subtracting the echo-estimate digital signal from the initial or first intermediate digital signal.
 76. A transceiver system as in claim 75 wherein: the adding/subtracting element in the digital echo-cancelling circuitry is substantially the same element as the adding/subtracting element in the crosstalk-cancelling circuitry; and the first intermediate digital signal is substantially the same signal as the crosstalk-cancellation intermediate digital signal such that the echo-reduced digital signal is substantially the same signal as the crosstalk-reduced digital signal.
 77. A transceiver system as in claim 60 wherein the receiver further includes a digital equalizer for adaptively equalizing the initial digital signal, or a third intermediate digital signal generated from the initial digital signal, to produce an equalized digital signal with reduced intersymbol interference.
 78. A transceiver system as in claim 60 wherein the receiver further includes an analog equalizer for adaptively equalizing the input analog signal, or a third intermediate analog signal generated from the input analog signal, to produce an equalized analog signal with reduced intersymbol interference.
 79. A transceiver system as in claim 78 wherein the receiver further includes a digital equalizer for adaptively equalizing the initial digital signal, or a third intermediate digital signal generated from the initial digital signal, to produce an equalized digital signal with further reduced intersymbol interference.
 80. A method comprising: transmitting a primary symbol-information-carrying output signal; receiving a primary symbol-information-carrying input analog signal that includes an echo of the output signal; adaptively operating on the input analog signal, or on a first intermediate analog signal generated from the input analog signal, to produce an echo-reduced analog signal in which the echo is reduced; converting the echo-reduced analog signal, or a second intermediate analog signal generated from the echo-reduced analog signal, into an initial digital signal; adaptively operating on the initial digital signal, or on a first intermediate digital signal generated from the initial digital signal, to produce an echo-reduced digital signal in which the echo is further reduced; decoding the echo-reduced digital signal, or a second intermediate digital signal generated from the echo-reduced digital signal, into a stream of symbols; and, during conversion of the input analog signal into the stream of symbols, adaptively adjusting echo-filtering characteristics that are used in the adaptively operating acts to produce the echo-reduced analog and digital signals.
 81. A method as in claim 80 wherein the adaptively adjusting act comprises adaptively adjusting the echo-filtering characteristics used in one of the adaptively operating acts in response to an error signal generated by decoding the echo-reduced digital signal or a further digital signal generated from the echo-reduced digital signal.
 82. A method as in claim 81 wherein the error signal varies at any time during the method according to the difference between (i) the echo-reduced or further digital signal at that time and (ii) a corresponding one of an alphabet of predefined symbols from which the stream of symbols is substantially formed, the corresponding predefined symbol being produced by decoding the echo-reduced or further digital signal at that time.
 83. A method comprising: transmitting a primary symbol-information-carrying output signal; receiving a primary symbol-information-carrying input analog signal that includes an echo of the output signal; adaptively operating on the input analog signal, or on a first intermediate analog signal generated from the input analog signal, to produce an echo-reduced analog signal in which the echo is reduced; converting the echo-reduced analog signal, or a second intermediate analog signal generated from the echo-reduced analog signal, into an initial digital signal; adaptively operating on the initial digital signal, or on a first intermediate digital signal generated from the initial digital signal, to produce an echo-reduced digital signal in which the echo is further reduced; decoding the echo-reduced digital signal, or a second intermediate digital signal generated from the echo-reduced digital signal, into a stream of symbols; and, during conversion of the input analog signal into the stream of symbols, adaptively adjusting echo-filtering characteristics that are used in the adaptively operating acts to produce the echo-reduced analog and digital signals, the adaptively adjusting act comprising adaptively adjusting the echo-filtering characteristics used in one of the adaptively operating acts in response to an error signal generated by decoding the echo-reduced digital signal or a further digital signal generated from the echo-reduced digital signal, the error signal varying at any time during the method according to the difference between (i) the echo-reduced or further digital signal at that time and (ii) a corresponding one of an alphabet of predefined symbols from which the stream of symbols is substantially formed, the corresponding predefined symbol being produced by decoding the echo-reduced or further digital signal at that time, the decoding to produce the predefined symbols used in generating the error signal being performed along a different signal processing path than the decoding to generate the stream of symbols.
 84. A transceiver system as in claim 36 further including circuitry for correcting for baseline signal wander.
 85. A transceiver system as in claim 60 further including circuitry for correcting for baseline signal wander. 